Spectroscopy

Spectroscopy (from Lat. spectrum, an appearance, and Gr. o-KovEiv, to see), that branch of physical science which has for its province the investigation of spectra, which may, for our present purpose, be regarded as the product of the resolution of composite luminous radiations into more homogeneous components. The instruments which effect such a resolution are called spectroscopes.

The Five-foot Spectroheliograph of the Mount Wilson Solar Observatory (camera lens, camera slit and plate carrier in section).

## 1\. Introductory

The announcement of the first discoveries made through the application of spectroscopy, then called spectrum analysis, appealed to the imagination of the scientific world because it revealed a method of investigating the chemical nature of substances independently of their distances: a new science was thus created, inasmuch as chemical analysis could =rT? == be applied to the sun and other stellar bodies. But the beautiful currents, but in the higher region shown by the hydrogen photographs the distribution of the dark flocculi suggested the operation of definite forces, though their nature remained obscure until the spring of 1908. At that time monochromatic photographs of the sun were first made on Mount Wilson with the red (Ha) line of hydrogen, previous hydrogen photographs having been taken with H/3, Hy or HS in the blue or violet. On account of the relatively great strength of Ha at a considerable distance from the photosphere, the new photographs recorded flocculi at high levels previously unexplored. The forms of these flocculi show that all sun-spots are vortical in nature, and are probably analogous to terrestrial cyclones or tornadoes. Most of the solar vortices indicate clockwise rotation in the southern hemisphere and counter-clockwise rotation in the northern, as in the case of terrestrial cyclones. But frequent exceptions have been observed in which the direction of rotation is reversed. The study of these vortices has led to the discovery of a magnetic field in sun-spots, apparently caused by electric convection in the vortices.

It is evident that by the use of a spectroheliograph of sufficiently high dispersion, photographs may be taken of vapours in the sun represented by lines narrower than those of calcium and hydrogen. Such work has been in progress both at Mount Wilson and at Meudon, and the erection of a spectroheliograph of 75 ft. focal length on Mount Wilson was at the end of 1908 contemplated for an early date.

Descriptions of spectroheliographs by Hale, Deslandres, Newall and others, may be found in various papers in Astronomy and Astrophysics, Astrophysical Journal, Comptes rendus, Bulletin astronomique, and other periodicals. (G. E. H.) simplicity of the first experiments, pointing apparently to the conclusion that each element had its characteristic and invariable spectrum whether in the free state or when combined with other bodies, was soon found to be affected by complications which all the subsequent years of study have not completely resolved. Compound bodies, we now know, have their own spectra, and only when dissociation occurs can the compound show the rays characteristic of the element: this perhaps was to be expected, but it came as a surprise and was not readily believed, that elements, as a rule, possess more than one spectrum according to the physical conditions under which they become luminous. Spectrum analysis thus passed quickly out of the stage in which its main purpose was " analysis " and became our most delicate and powerful method of investigating molecular properties; the old name being no longer appropriate, we now speak of the science of " Spectroscopy." 1 Within the limit of this article it is not possible to give a complete account of this most intricate branch of physics; the writer therefore confines himself to a summary of the problems which now engage scientific attention, referring the reader for details to H. Kayser's excellent and complete Handbuch der Spectroscopie. 2. Instrumental. - The spectroscope is an instrument which allows us to examine the vibrations sent out by a radiating source: it separates the component parts if they are homogeneous, i.e. of definite periodicity, and then also gives us the distribution of intensity along the homogeneous constituents. This resolution into simple periodic waves is arbitrary in the same sense as is the decomposition of forces along assumed 1 The present writer believes that he was the first to introduce the word " Spectroscopy " in a lecture delivered at the Royal Institution in 1882 (Proceedings, vol. ix.).

axes; but, in the same way also the results are correct if the resolution is treated as an analytical device and in the final result account is taken of all the overlapping components. Spectroscopes generally consist of three parts: (I) the collimator; (2) the analysing appliance, (3) the telescope. The slit of the collimator confines the light to a nearly linear source, the beam diverging from each point of the source being subsequently made parallel by means of a lens. The parallelism, which is required to avoid aberrations, otherwise introduced by the prism or grating, may often be omitted in instruments of small power. The lens may then be also dispensed with, and the whole collimator becomes unnecessary if the luminous source is narrow and at a great distance, as for instance in the case of the crescent of the sun near the second and third contact of a total solar eclipse. The telescope serves to examine the image of the slit and to measure the angular separation of the different slit images; when photographic methods are employed the telescope is replaced by a camera.

The analysing appliance constitutes the main feature of a spectroscope. It may consist of one of the following: a. A prism or a train of prisms. These are employed in instruments of small power, especially when luminosity is a consideration; but their advantage in this respect is to a great extent lost, when, in order to secure increased resolving power, the size of the prisms, or their number, is unduly increased.

b. A grating. Through H. A. Rowland's efforts the construction of gratings has been improved to such an extent that their use is becoming universal whenever great power or accuracy is required. By introducing the concave grating which (see Diffraction Of Light, § 8) allows US to dispense with all lenses, Rowland produced a revolution in spectroscopic measurement. At present we have still to content ourselves with a much diminished intensity of light when working with gratings, but there is some hope that the efforts to concentrate the light into one spectrum will soon be successful.

c. An echelon grating. Imagine a horizontal section of a beam of light, and this section divided into a number of equal parts. Let somehow or other retardations be introduced so that the optical length of the successive parts increases by the same quantity nX, n being some number and X the wave-length. If on emergence the different portions he brought together at the focus it is obvious that the optical action must be in every respect similar to that of a grating when the nth order of spectrum is considered. A. Michelson produced the successive retardations by inserting step-by-step plates of glass of equal thickness so that the different portions of the beam traversed thicknesses of glass equal to nX, 2nX, 3nX, ... NA. The optical effect as regards resolving power is the same as with a grating of N lines in the nth order, but, nearly all the light not absorbed by the glass may be concentrated in one or two orders.' d. Some other appliance in which interference with long difference of path is made use of, such as the interferometer of Fabry and Perot, or Lummer's plate (see Interference Of Light) .

The echelon and interferometer serve only a limited purpose, but must be called into action when the detailed structure of lines is to be examined. For the study of Zeeman effects (see Magneto-Optics) the echelon seems specially adapted, while the great pliability of 'Fabry and Perot's methods, allowing a clear interpretation of results, is likely to secure them permanently an established place in measurements of precision.

The power of a spectroscope to perform its main function, which is to separate vibrations of different but closely adjacent frequencies, is called its " resolving power." The limitation of power is introduced as in all optical instruments, by the finiteness of the length of a wave of light which causes the image of an indefinitely narrow slit to spread out over a finite width in the focal plane of the observing telescope. The so-called " diffraction " image of a homogeneously illuminated slit shows a central band limited on either side by a line along which the ' Michelson, Astrophys. Journ. (1898), 8, p. 36; A. Schuster, Theory of Optics, p. 115.

intensity is zero, and this band is accompanied by a number of fainter images corresponding to the diffraction of a star image in a telescope. Lord Rayleigh, to whom we owe the first general discussion of the theory of the spectroscope, found by observation that if two spectroscopic lines of frequencies n1 and n, are observed in an instrument, they are just seen as two separate lines when the centre of the central diffraction band of one coincides with the first minimum intensity of the other. In that case the image of the double line shows a diminution of intensity along the centre, just sufficient to give a clear impression that we are not dealing with a single line, and the intensity at the minimum is 0.81 of that at the point of maximum illumination. We may say therefore that if the difference between the frequencies n 1 and n, of the two waves is such that in the combined image of the slit the intensity at the minimum between -the two maxima falls to 0.81, the lines are just resolved and n l /(n l n 2 ) may then be called the resolving power. There is something arbitrary in this definition, but as the practical importance of the question lies in the comparison between instruments of different types, the exact standard adopted is of minor importance, the chief consideration being simplicity of application. Lord Rayleigh's expression for the resolving power of different instruments is based on the assumption that the geometrical image of the slit is narrow compared with the width of the diffraction image. This condition is necessary if the full power of the instrument is to be called into action. Unfortunately considerations of luminosity compel the observer often to widen the slit much beyond the range within which the theoretical value of resolving power holds in practice. The extension of the investigation to wide slits was first made by the present writer in the article " Spectroscopy " in the 9th edition of the Encyclopaedia Britannica. Reconsideration of the subject led him afterwards to modify his views to some extent, and he has since more fully discussed the question. 2 Basing the investigation on the same criterion of resolution as in the case of narrow slits, we postulate for both narrow and wide slits that two lines are resolved when the intensity of the combined image falls to a value of o8ro in the centre between the lines, the intensity at the maxima being unity. We must now however introduce a new criterion the " purity " and distinguish it from the resolving power: the purity is defined by n l /(n l n2), where n 1 and n, are the frequencies of two lines such that they would just be resolved with the width of slit used. With an indefinitely narrow slit the purity is equal to the resolving power. As purity and resolving power are essentially positive quantities, n i in the above expression must be the greater of the two frequencies. With wide slits the difference n1 - n2  depends on their width. If we write P=p R where P denotes the purity and R the resolving power, we may call p the " purityfactor. " In the paper quoted the numerical values of p are given for different widths of slit, and a table shows to what extent the loss of purity due to a widening of the slit is accompanied by a gain in luminosity. The general results may be summarized as follows: if the width of the slit is equal to fX/4D (where X is the wave-length concerned, D the diameter of the collimator lens, and f its focal length) practically full resolving power is obtained and a further narrowing of the slit would lead to loss of light without corresponding gain. We call a slit of this width a " normal slit. " With a slit width equal to twice the normal one we lose 6% of resolution, but obtain twice the intensity of light. With a slit equal in width to eight times the normal one the purity is reduced to o45R, so that we lose rather more than half the resolving power and increase the light 3.7 times. If we widen the slit still further rapid loss of purity results, with very little gain in light, the maximum luminosity obtainable with an indefinitely wide slit being four times that obtained with the normal one. It follows that for observations in which light is a consideration spectroscopes should be used which give about twice the resolving power of that actually required; we may then use a slit having a width of nearly eight times that of the normal one.

2 Astrophys. Journ. (1905), 21, p. 197.

Theoretical resolving power can only be obtained when the whole collimator is filled with light and further (as pointed out by Lord Rayleigh in the course of discussion during a meeting of the " Optical Convention " in London, 1905) each portion of the collimator must be illuminated by each portion of the luminous source. These conditions may be generally satisfied by projecting the image of the source on the slit with a lens of sufficient aperture. When the slit is narrow light is lost through diffraction unless the angular aperture of this condensing lens, as viewed from the slit, is considerably greater than that of the collimator lens.

When spectroscopes are used for stellar purposes further considerations have to be taken account of in their construction; and these are discussed in a paper by H. F. Newall.1 3. Spectroscopic Measurements and Standards of Wave-Length.-  All spectroscopic measurement should be reduced to wavelengths or wave-frequencies, by a process of interpolation between lines the wave-lengths of which are known with sufficient accuracy. The most convenient unit is that adopted by the International Union of Solar Research and is called an Angstrom (A); and is equal to i 08 cms. A. Perot and C. Fabry, employing their interferometer methods, have compared the wave-length of the red cadmium line with the standard metre in Paris and found it to be equal to 6438.4696 A, the observations being taken in dry air at 18° C and at a pressure of 76 cms. (g = 980.665). This number agrees singularly well with that determined in 1893 by Michelson, who found for the same line 6438-470o. Perot's number is now definitely adopted to define the Angstrom, and need never be altered, for should at some future time further researches reveal a minute error, it will be only necessary to change slightly the temperature or pressure of the air in which the wave-length is measured. A number of secondary standards separated by about 50 A, and tertiary standards at intervals of from 5 to 10 A have also been determined. By means of these, spectroscopists are enabled to measure by interpolation the wave-length of any line they may wish to determine. Interpolation is easy in the case of all observations taken with a grating. In the case of a prism some caution is necessary unless the standards used are very close together. The most convenient and accurate formula of interpolation seems to be that discovered by J. F. Hartmann. If D is the measured deviation of a ray, and Do, Xo, c and a are four constants, the equation A=Ao-{ (D - D °) l /a seems to represejlt the connexion between deviation and wavelength with considerable accuracy for prisms constructed with the ordinary media.

The constant a has the same value I 2 for crown and flint glass, so that there are only three disposable constants left. In many cases it is sufficient to substitute unity for a and write X-X0HD -D0', which gives a convenient formula, which in this form was first used by A. Cornu. If within the range5100-3700A, the constants are determined once for all, the formula seems capable of giving by interpolation results accurate to o2 A, but as a rule the range to which the formula is applied will be much less with a corresponding gain in the accuracy of the results.

Every observer should not only record the resolving power of the instrument he uses, but also the purity-factor as defined above. The resolving power in the case of gratings is simply mn, where m is the order of spectrum used, and n the total number of lines ruled on the grating. In the case of prisms the resolving power ist (dµ/dX), where t is the effective thickness of the medium traversed by the ray. If 1 2 and t l are thicknesses traversed by the extreme rays, t = t 2 - t,, and if, as is usually the case, the prism is filled right up to its refraction cap, = o, and t becomes equal to the greatest thickness of the medium which is made use of. When compound prisms are used in which, 1 Monthly Notices R.A.S. (1905), 65, p. 605.

for the purpose of obtaining smaller deviation, one part of the compound acts in opposition to the other, the resolving power of the opposing portion must be deducted in calculating the power of the whole. Opticians should supply sufficient information of the dispersive properties of their materials to allow dµ/dX to be calculated easily for different parts of the spectrum.

The determination of the purity-factor requires the measurement of the width of the slit. This is best obtained by optical means. The collimator of a spectroscope should be detached, or moved so as to admit of the introduction of an auxiliary slit at a distance from the collimator lens equal to its focal length. If a source of light be placed behind the auxiliary slit a parallel beam of light will pass within the collimator and fall on the slit the width of which is to be measured. With fairly homogeneous light the diffraction pattern may be observed at a distance, varying with the width of the slit from about the length of the collimator to one quarter of that length. From the measured distances of the diffraction bands the width of the slit may be easily deduced.

4\. Methods of Observation and Range of Wave-Lengths. - Visual  observation is limited to the range of frequencies to which our eyes are sensitive. Defining oscillation as is usual in spectroscopic measurement by wave-length, the visible spectrum is found to extend from about 7700 to 3900 A. In importance next to visual observation, and in the opinion of some, surpassing it, is the photographic method. We are enabled by means of it to extend materially the range of our observation, especially if the ordinary kinds of glass, which strongly absorb ultraviolet light, are avoided, and, when necessary, replaced by quartz. It is in this manner easy to reach a wave-length of 3000 A, and, with certain precautions, 1800 A. At that point, however, quartz and even atmospheric air become strongly absorbent and the expensive fluorspar becomes the only medium that can be used. Hydrogen still remains transparent. The beautiful researches of V. Schumann 2 have shown, however, that with the help of spectroscopes void of air and specially prepared photographic plates, spectra can be registered as far down as lzoo A. Lyman more recently has been able to obtain photographs as far down as 1030 A with the help of a concave grating placed in vacuo. 3 Although the vibrations in the infra-red have a considerably greater intensity, they are more difficult to register than those in the ultra-violet. Photographic methods have been employed successfully by Sir W. Abney as far as 20,000 A, but long exposures are necessary. Bolometric methods may be used with facility and advantage in the investigation of the distribution of intensities in continuous or semi-continuous spectra but difficulties are met with in the case of line spectra. Good results in this respect have been obtained by B. W. Snow' and by E. P. Lewis,' lines as far as 11,500 having been measured by the latter. More recently F. Paschen 6 has further extended the method and added a number of infra-red lines to the spectra of helium, argon, oxygen and other elements. In the case of helium one line was found with a wave-length of 20,582 A. C. V. Boys' microradiometer has occasionally been made use of, and the extreme sensitiveness of the Crookes' radiometer has also given excellent results in the hands of H. Rubens and E. F. Nichols. In the opinion of the writer the latter instrument will ultimately replace the bolometer, its only disadvantage being that the radiations have to traverse the side of a vessel, and are therefore subject to absorption. In order to record line spectra it is by no means necessary that the receiving instrument (bolometer or radiometer) should be linear in shape, for the separation of adjacent lines may be obtained if the linear receiver be replaced by a narrow slit in a screen placed at the focus of the condensing lens. The sensitive vane or strip may then be placed behind the slit; its width will not affect the resolving power though there may be a diminution of sensitiveness. The longest waves Wied. Annalen (1901), 5, p. 349.

Astrophys. Journ. (1906), 23, p. 181.

4 Wied. Annalen (1892),7, p. 208.

5 Astrophys. Journ. (1895), 2, p. I.

Drude Annalen (1908), 2 7, p. 537 and (1909), 29.

observed up to the present are those recorded by H. Rubens and E. Aschkinass 1 (o061 cros. or 61o,000 A).

5\. Methods of Rendering Gases Luminous. - The extreme flexibility of the phenomena shown by radiating gases renders it a matter of great importance to examine them under all possible conditions of luminosity. Gases, like atmospheric air, hydrogen or carbon dioxide do not become luminous if they are placed in tubes, even when heated up far beyond white heat as in the electric furnace. This need not necessarily be interpreted as indicating the impossibility of rendering gases luminous by temperature only, for the transparency of the gas for luminous radiations may be such that the emission is too weak to be detected. When there is appreciable absorption as in the case of the vapours of chlorine, bromine, iodine, sulphur, selenium and arsenic, luminosity begins at a red heat. Thus G. Salet observed that iodine gives a spectrum of bright bands when in contact with a platinum spiral made white hot by an electric current, and J. Evershed 3 has shown that in this and other cases the temperature at which emission becomes appreciable is about 700°. It is only recently that owing to the introduction of carbon tubes heated electrically the excitement of the luminous vibrations of molecules by temperature alone has become an effective method for the study of their spectra even in the case of metals. Hitherto we were entirely and still are generally confined to electrical excitation or to chemical action as in the case of flames.

In the ordinary laboratory the Bunsen flame has become universal, and a number of substances, such as the salts of the alkalis and alkaline earths, show characteristic spectra when suitably placed in it. More information may be gained with the help of the oxyhydrogen flame, which with its higher temperature has not been used as frequently as it might have been, but W. N. Hartley has employed it with great success, and in cyanite (a silicate of aluminium) has found a material which is infusible at the temperature of this flame, and is therefore suitable to hold the substance which it is desired to examine. An interesting and instructive manner of introducing salts into flames was discovered by A. Gouy, who forced the air before it entered the Bunsen burner, through a spray produce containing a salt in solution. By this method even such metals as iron and copper may be made to show some of their characteristic lines in the Bunsen burner. The spectra produced under these circumstances have been studied in detail by C. de Watteville.4 Of more frequent use have been electric methods, owing to the greater intensity of the radiations which they yield. Especially when large gratings are employed do we find that the electric arc alone seems sufficient to give vibrations of the requisite power. The metals may be introduced into the arc in various ways, and in some cases where they can be obtained in sufficient quantity the metallic electrodes may be used in the place of carbon poles.

The usual method of obtaining spectra by the discharges from a Ruhmkorff coil or Wimshurst machine needs no description. The effects may be varied by altering the capacity and self-induction of the circuit which contains the spark gap. The insertion of self-induction has the advantage of avoiding the lines due to the gas through which the spark is taken, but it introduces other changes in the nature of the spark, so that the results obtained with and without self-induction are not directly comparable. Count Gramont 5 has been able to obtain spectro scopic evidence of the metalloids in a mineral by employing powerful condensers and heating the electrodes in an oxyhydro gen flame when these (as is often the case) are not sufficiently conducting.

When the substance to be examined spectroscopically is in solution the spark may be taken from the solution, which must then be used as kathode of air. The condenser is in this case 1 Wied. Annalen (1898), 65, p. 241.

\- 2 Ann. Chim. Phys. (1873), 28.

Phil. Mag. (1895), 39, p. 460.

Phil. Trans. (1904), 204, A. p. 139.

5 Comptes rendus, vols. 121, 122, 124.

not necessary, in fact better results are obtained without it.. Lecoq de Boisbaudran has applied this method with considerable success, and it is to be recommended whenever only small electric power is at the disposal of the observer. To diminish the resistance the current should pass through as small a layer of liquid as possible. It is convenient to place the liquid in a short tube., a platinum wire sealed in at the bottom to convey the current reaching to the level of the open end. If a thickwalled capillary tube is passed over the platinum tube and its length so adjusted that the liquid rises in it by capillary action just above the level of the tube, the spectrum may be examined directly, and the loss of light due to the passage through the partially wetted surface of the walls of the tube is avoided.

For the investigation of the spectra of gases at reduced pressures the so-called Plucker tubes (more generally but incorrectly called Geissler tubes) are in common use. When the pressure becomes very low, inconvenience arises owing to the difficulty of establishing the discharge. In that case the method introduced by J. J. Thomson might with advantage be more frequently employed. Thomson 6 places spherical bulbs inside thick spiral conductors through which the oscillating discharge of a powerful battery is led. The rapid variation in the intensity of the magnetic field causes a brilliant electrodeless discharge which is seen in the form of a ring passing near the inner walls of the bulb when the pressure is properly adjusted. A variety of methods to render gases luminous should be at the command of the investigator, for nearly all, show some distinctive peculiarity and any new modification generally results in fresh facts being brought to light. Thus E. Goldstein 7 was able to show that an increase in the current density is capable of destroying the well-known spectra of the alkali metals, replacing them by quite a new set of lines.

6\. Theory of Radiation. - The general recognition of spectrum analysis as a method of physical and chemical research occurred simultaneously with the theoretical foundation of the connexion between radiation and absorption. Though the experimental and theoretical developments were not necessarily dependent on each other, and by far the larger proportion of the subject which we now term " Spectroscopy " could stand irrespective of Gustav Kirchhoff's thermodynamical investigations, there is no doubt that the latter was, historically speaking, the immediate cause of the feeling of confidence with which the new branch of science was received, for nothing impresses the scientific world more strongly than just that little touch of mystery which attaches to a mathematical investigation which can only be understood by the few, and is taken on trust by the many, provided that the author is a man who commands general confidence. While Balfour Stewart's work on the theory of exchanges was too easily understood and therefore too easily ignored, the weak points in Kirchhoff's developments are only now beginning to be perceived. The investigations both of Balfour Stewart and of Kirchhoff are based on the idea of an enclosure at uniform temperature and the general results of the reasoning centre in the conclusion that the introduction of any body at the same temperature as the enclosure can make no difference to the streams of radiant energy which we imagine to traverse the enclosure. This result, which, accepting the possibility of having an absolutely opaque enclosure of uniform temperature, was clearly proved by Balfour Stewart for the total radiation, was further extended by Kirchhoff, who applied it (though not with mathematical rigidity as is sometimes supposed) to the separate wave-lengths. All Kirchhoff's further conclusions are based on the assumption that the radiation transmitted through a partially transparent body can be expressed in term,s. of two independent factors (i) an absorption of the incident radiation, and (2) the radiation of the absorbing medium, which takes place equally in' all directions. It is assumed further that the absorption is proportional to the incident radiation and (at any rate approximately) independent of the temperature, while the radiation is assumed to be a function of the temperature 6 Phil. Mag. 32, pp. 3 21, 445.

7 Vertr. d. phys. Ges. (1904), 9, p. 321.

only and independent of the temperature of the enclosure. This division into absorption and radiation is to some extent artificial and will have to be revised when the. p henomena of radiation are placed on a mechanical basis. For our present purpose it is only necessary to point out the difficulty involved in the assumption that the radiation of a body is independent of the temperature of the enclosure. The present writer drew attention to this difficulty as far back as 1881, 1 when he pointed out that the different intensities of different spectral lines need not involve the consequence that in an enclosure of uniform temperature the energy is unequally partitioned between the corresponding degrees of freedom. When the molecule is losing energy the intensity of each kind of radiation depends principally on the rapidity with which it can be renewed by molecular impacts. The unequal intensities observed indicate a difference in the effectiveness of the channels through which energy is lost, and this need not be connected with the ultimate state of equilibrium when the body is kept at a uniform temperature. For our immediate purpose these considerations are of importance inasmuch as they bear on the question how far the spectra emitted by gases are thermal effects only. We generally observe spectra under conditions in which dissipation of energy takes place, and it is not obvious that we possess a definition of temperature which is strictly applicable to these cases. When, for instance, we observe the relation of the gas contained in a Plucker tube through which an electric discharge is passing, there can be little doubt that the partition of energy is very different from what it would be in thermal equilibrium. In consequence the question as to the connexion of the spectrum with the temperature of the gas seems to the present writer to lose some of its force. We might define temperature in the case of a flame or vacuum tube by the temperature which a small totally reflecting body would tend to take up if placed at the spot, but this definition would fail in the case of a spark discharge. Adopting the definition we should have no difficulty in proving that in a vacuum tube gases may be luminous at very low temperatures, but we are doubtful whether such a conclusion is very helpful towards the elucidation of our problem. Radiation is a molecular process, and we can speak of the radiation of a molecule but not of its temperature. When we are trying to bring radiation into connexion with temperature, we must therefore take a sufficiently large group of molecules and compare their average energies with the average radiation. The question arises whether in a vacuum discharge, in which only a comparatively small proportion of the molecules are affected, we are to take the average radiation of the affected portion or include the whole lot of molecules, which at any moment are not concerned in the discharge at all. The two processes would lead to entirely different results. The problem, which, in the opinion of the present writer, is the one of interest and has more or less definitely been in the minds of those who have discussed the subject, is whether the type of wave sent out by a molecule only depends on the internal energy of that molecule, or on other considerations such as the mode of excitement. The average energy of a medium containing a mixture of dissimilar elements possesses in this respect only a very secondary interest.

We must now inquire a little more closely into the mechanical conception of radiation. According to present ideas, the wave originates in a disturbance of electrons within the molecules. The electrons responsible for the radiation are probably few and not directly involved in the structure of the atom, which according to the view at present in favour, is itself made up of electrons. As there is undoubtedly a connexion between thermal motion and radiation, the energy of these electrons within the atom must be supposed to increase with temperature. But we know also that in the complete radiation of a white body the radiative energy increases with the fourth power of the absolute temperature. Hence a part of what must be included in thermal energy is not simply proportional to temperature as is commonly assumed. The energy of radiation resides in the medium and not in the molecule. Even at the 1 Phil. Mag. (1881), 12, p. 261.

highest temperatures at our command it is small compared with the energy of translatory motion, but as the temperature increases, it must ultimately gain the upper hand, and if there is anywhere such a temperature as that of several million degrees, the greater part of the total energy of a body will be outside the atom and molecular motion ultimately becomes negligible compared with it. But these speculations, interesting and important as they are, lead us away from our main subject.

Considering the great variety of spectra, which one and the same body may possess, the idea lies near that free electrons may temporarily attach themselves to a molecule or detach 'themselves from it, thereby altering the constitution of the vibrating system. This is most likely to occur in a discharge through a vacuum tube and it is just there that the greatest variety of spectra is observed.

It has been denied by some that pure thermal motion can ever give rise to line spectra, but that either chemical action or impact of electrons is necessary to excite the regular oscillations which give rise to line spectra. There is no doubt that the impact of electrons is likely to be effective in this respect, but it must be remembered that all bodies raised to a sufficient temperature are found to eject electrons, so that the presence of the free electrons is itself a consequence of temperature. The view that visible radiation must be excited by the impact of such an electron is therefore quite consistent with the view that there is no essential difference between the excitement due to chemical or electrical action and that resulting from a sufficient increase of temperature.

Chemical action has frequently been suggested as being a necessary factor in the luminosity of flame, not only in the sense that it causes a sufficient rise of temperature but as furnishing some special and peculiar though undefined stimulus. An important experiment by C. Gunther 2 seems however to show that the radiation of metallic salts in a flame has an intensity equal to that belonging to it in virtue of its temperature.

If a short length of platinum wire be inserted vertically into a lighted Bunsen burner the luminous line may be used as a slit and viewed directly through a prism. When now a small bead of a salt of sodium or lithium is placed in the flame the spectrum of the white hot platinum is traversed by the dark absorption of the D lines. This is consistent with Kirchhoff's law and shows that the sodium in a flame possesses the same relative radiation and absorption as sodium vapour heated thermally to the temperature of the flames. According to independent experiments by Paschen the radiation of the D line sent out by the sodium flame of sufficient density is nearly equal to that of a black body at 'the same temperature. 3 Other more recent experiments confirm the idea that the radiation of flames is mainly determined by their temperature.

The definition of temperature given above, though difficult in the case of a flame and perhaps still admissible in the case of an electric arc, becomes precarious when applied to the disruptive phenomena of a spark discharge. The only sense in which we might be justified in using the word temperature here is by taking account of the energy set free in each discharge and distributing it between the amount of matter to which the energy is supplied. With a guess at the specific heat we might then calculate the maximum temperature to which the substance might be raised, if there were no loss by radiation or otherwise. But the molecules affected by a spark discharge are not in any sense in equilibrium as regards their partition of energy and the word temperature " cannot therefore be applied to them in the ordinary sense. We might probably with advantage find some definition of what may be called " radiation temperature " based on the relation between radiation and absorption in Kirchhoff's sense, but further information based on experimental investigation is required.

## 7\. Limits of Homogeneity and Structure of Lines

As a first `approximation we may say that gases send out homogeneous 2 Wied. Ann. (1877), 2, P. 477' Ibid. (1894), 5 1, p. 40.

radiations. A homogeneous oscillation is one which for all time is described by a circular function such as sin(nt+ a), t being the time and n and a constants. The qualification that the circular function must apply to all time is important, and unless it is recognized as a necessary condition of homogeneity, confusion in the more intricate problems or radiation becomes inevitable. Thus if a molecule were set into vibration at a specified time and oscillated according to the above equation during a finite period, it would not send out homogeneous vibrations. In interpreting the phenomena observed in a spectroscope, it is necessary to remember that the instrument, as pointed out by Lord Rayleigh, is itself a producer of homogeneity within the limits defined by its resolving power. A spectroscope may be compared to a mechanical harmonic analyser which when fed with an irregular function of one variable represented by a curve supplies us with the sine curves into which the original function may be resolved. This analogy is useful because the application of Fourier's analysis to the optical theory of spectroscopes has been doubted, and it may be urged in answer to the objections raised that the instrument acts in all respects like a mechanical analyser,' the applicability of which has never been called into question.

A limit to homogeneity of radiation is ultimately set by the so-called Doppler effect, which is the change of wave-length due to the translatory motion of the vibrating molecule from or towards the observer. If N be the frequency of a homogeneous vibration sent out by a molecule at rest, the apparent frequency will be N (1 v/ V), where V is the velocity of light and v is the velocity of the line of sight, taken as positive if the distance from the observer increases. If all molecules moved with the velocity of mean square, the line would be drawn out into a band having on the frequency scale a width 2Nv/V, where v is now the velocity of mean square. According to Maxwell's law, however, the number of molecules having a velocity in the line of sight lying between v and vd-dv is proportional to e-1 3v2 dv, where (3 is equal to 312u 2; for v=u, we have therefore the ratio in the number of molecules having velocity u to those having no velocity in the line of sight e-0/1 2 =-- e-z = 22. We may therefore still take 2Nu/V to be the width of the band if we define its edge to be the frequency at which its intensity has fallen to 22% of the central intensity. In the case of hydrogen rendered luminous in a vacuum tube we may put approximately u equal to 2000 metres per second, if the translatory motion of the luminous molecules is about the same as that at the ordinary temperature. In that case Au/V or the half width of the band measured in wave lengths would be .105 A, or, for the red line, the half width would be 0.044 A. Michelson, who has compared the theoretical widening with that found experimentally by means of his interferometer, had to use a somewhat more complicated expression for the comparison, as his visibility curve does not directly give intensities for particular frequencies but an integral depending on a range of frequency? He finds a remarkable agreement between the theoretical and experimental values, which it would be important to confirm with the more suitable instruments which are now at our disposal, as we might in this way get an estimate of the energy of translatory motion of the luminous molecules. If the motion were that of a body at white heat, or say a temperature of loco, the velocity of mean square would be 39co metres per second and the apparent width of the band would be doubled. Michelson's experiments therefore argue in favour of the view that the luminescence in a vacuum tube is similar to that produced by phosphorescence where the translatory energy does not correspond to the oscillatory energy - but further experiments are desirable. The experimental verification of the change of wave-length due to a source moving in the line of sight has been realized in the laboratory by A. Belopolsky and Prince Galitzin, who substituted for the source an image formed of a stationary object in a rapidly moving mirror.

'Phil. Mag. (1894), 37, p. 509.

Cf. Rayleigh, Phil. Mag. (1899), 2 7, p. 298; Michelson, Phil. Mag. (1892), 34, p. 280.

The homogeneity of vibration may also be diminished by molecular impacts, but the number of shocks in a given time depends on pressure and we may therefore expect to diminish the width of a line by diminishing the pressure. It is not, however, obvious that the sudden change of direction in the translatory motion, which is commonly called a molecular shock, necessarily also affects the phase of vibration. Experiments which will be discussed in § to seem to show that there is a difference in this respect between the impacts of similar and those of dissimilar molecules. When the lines are obtained under circumstances which tend towards sharpness and homogeneity they are often found to possess complicated structures, single lines breaking up into two or more components of varying intensities. One of the most interesting examples is that furnished by the green mercury line, which when examined by a powerful echelon spectroscope splits up into a number of constituents which have been examined by several investigators. Six companions to the main lines are found with comparative ease and certainty and these have been carefully measured by Prince Galitzin, 3 H. Stansfield 4 and L. Janicki. 5 According to Stansfield there are three companion lines on either side of a central line, which consists of two lines of unequal brightness.

8\. Distribution of Frequencies in Line Spectra. - It is natural to consider the frequencies of vibrations of radiating molecules as analogous to the different notes sent out by an acoustical vibrator. The efforts which were consequently made in the early days of spectroscopy to discover some numerical relationship between the different wave lengths of the lines belonging to the same spectrum rather disregard the fact that even in acoustics the relationship of integer numbers holds only in special and very simple cases. Some corroboration of the simple law was apparently found by Johnstone Stoney, who first noted that the frequencies of three out of the four visible hydrogen lines are in the ratios 20: 27: 32. In other spectra such " harmonic " ratios were also discovered, but their search was abandoned when it was found that their number did not exceed that calculated by the laws of probability on the supposition of a chance distribution. 6 The next great step was made by J. J. Balmer, who showed that the four hydrogen lines in the visible part of the spectrum may be represented by the equation n = A(i - 4/s2), where n is the reciprocal of the wave-length and therefore proportional to the wave frequency, and s successively takes the values 3, 4, 5, 6. Balmer's formula received a striking confirmation when it was found to include the ultra-violet lines which were discovered by Sir William Huggins' in the photographic spectra of stars. The most complete hydrogen spectrum is that measured by Evershed 8 in the flash spectrum observed during a total solar eclipse, and contains thirty-one lines, all of which agree with considerable accuracy with the formula, if the frequency number n is calculated correctly by reducing the wave-length to vacuo.9 It is a characteristic of Balmer's formula that the frequency approaches a definite limit as s is increased, and it was soon discovered that in several other spectra besides hydrogen, series of lines could be found, which gradually come nearer and nearer to each other as they become fainter, and approach a definite limit. Such series ought all to be capable of being represented by a formula resembling that of Balmer, but so far the exact form of the series has not been established with certainty. The more important of the different forms suggested are as follow: .- 5 C 7, (H. Kayser and C. Runge). (2) n= A s)2 (J. R. Rydberg).

Bulletin Akad. St Petersburg (1907), p. 159.

4 Phil. Mag. (September, 1909), 18, p. 371.

' Ann. d. Phys. (1909), 2 9, p. 1833.

'A. Schuster, Proc. Roy. Soc. (1881), 21, p. 337.

' Phil. Trans. (1880), 171, p. 619.

8 Ibid (1891), 1 97, p. 381.

'The table so corrected will be found in C. Baly's Spectroscopy, P . 472 _ N (E. C. Pickering, generalized by T. N.

(3) n A (s+µ) +a Thiele).

(4) n=A (r+a+b/r2)2 (Ritz).

(5) n =A - (Hicks). (s+µ + a/s)° In all cases s represents the succession of integer numbers. In the last case we must put for r either s or s-1-1 according to the nature of the series, as will be explained further on. The first of the forms which contains three disposable constants did good service in the hands of their authors, but breaks down in important cases when odd powers of s have to be introduced in addition to the even powers. The second form contains two or three constants according as N is taken to have the same value for all elements or not. Rydberg favours the former view, but he does not attempt to obtain any very close approximation between the observed and calculated values of the frequencies. Equation (3), which E. C. Pickering' used in a special case, presently to be referred to, was put into a more general form by Thiele, who, however, assumes N to have the same value for all spectra, and not obtaining sufficient agreement, rejects the formula. J. Halm subsequently showed that if N may differ in different cases, the equation is a considerable improvement on Rydberg's. It then possesses four adjustable constants, and more can therefore be expected from it. All these forms are put into the shade by that which was introduced by Ritz, led thereto apparently by theoretical considerations. As he takes N to be strictly the same for all elements the equation has only three disposable constants A, a and b. It is found to be very markedly superior to the other equations. Its chief advantage appears, however, when the relationship between different series of the same element is taken into account. We therefore turn our attention to this relationship.

In the case of those elements in which we can represent the spectrum most completely by a number of series, it is generally. found that they occur in groups of three which are closely related to each other. They were called by H. Kayser and F. Paschen " Haupt serie," " ist Nebenserie," " 2nd Nebenserie," which is commonly translated " Principal series," "First subordinate series," " Second subordinate series." These names become inconvenient when, as is generally the case, each of the series splits into groups of two or three, and we have to speak of the second or third number of the first or second subordinate series. Moreover, a false impression is conveyed by the nomenclature, as the second subordinate series is much more closely related to the principal series than the first subordinate series. The present writer, therefore, in his Theory of Optics, adopted different names, and called the series respectively the " Trunk," the " Main Branch " and the " Side Branch," the main branch being identical with the second subordinate series; the limit of frequency for high values of s is called the " root " of the series, and it is found in all cases that the two branches have a common root at some point in the trunk. According to an important law discovered by Rydberg and shortly afterwards independently by the writer, the frequency of the common root of the two branches is obtained by subtracting the frequency of the root of the trunk from that of its least refrangible and strongest member. In the spectra of the alkali metals each line of the trunk is a doublet, and we may speak of a twin trunk springing out of the same root. In the same spectra the lines belonging to the two branches are also doublets. According to the above law the least refrangible member of the trunk being double, there must be two roots for the branches, and this is found to be the case. In fact the lines of each branch are also doublets, with common difference of frequency. There are, therefore, two main branches and two side branches, but these are not twins springing out of the same root, but parallel branches springing out of different though closely adjacent roots. It will also be noticed that the least refrangible of the doublets of the 1 Astrophys. Journ. (896), 4, 369.

2 Ibid. (1897), 65.

Trans. Ast. Soc. Edinburgh (1905), p. 551.

branches must according to the above law correspond to the most refrangible of the doublets of the trunk, and if the components of the doublets have different intensities the stronger components must lie on different sides in the trunk and branch series. This is confirmed by observation. Rydberg discovered a second relationship, which, however, involving the assumed equation connecting the different lines, cannot be tested directly as long as these equations are only approximate. On the other hand the law, once shown to hold approximately, may be used to test the sufficiency of a particular form of equation. These forms all agree in making the frequency negative when s falls below a certain value sp. Rydberg's second law states that if the main branch series is taken, the numerical value of np_I  corresponding to sp_ I is equal. to the frequency of the least refrangible member of the trunk series.

The two laws are best understood by putting the equations in the form given them by Rydberg.

For the trunk series write n s  N = (I +U) (s +12)'  and for the main branch series. n's  N ( I +µ) (s+o.)2 Here and N are constants, while s as before is an integer number.

The difference between the frequencies of the roots (s = co) is given by This is the first law.

If further in the two equations we put s =1, we obtain: n1 = This is the second law.

As has already been mentioned, the law is only verified very roughly, if Rydberg's form of equation is taken as correctly representing the series. The fact that the addition of the term introduced by Ritz not only gives a more satisfactory representation of each series, but verifies the above relationship with a much closer degree of approximation, proves that Ritz's equation forms a marked step in the right direction. According to him, the following equations represent the connexion between the lines of the three related series.

Trunk series: t N = [s +al +b/s 1 [1 5 +a1 +b'/(I.5)2}2 Main Branch Series: t ytr' - I I N [2 + al + 6/29 2 [r+al  Side Branch Series: t nT =  N [2 +al+6,/22]2 [s+c+d,s92  Here s stands for an integer number beginning with 2 for the trunk and 3 for the main branch, and r represents the succession of numbers 1 5, 5, 3 5, &c. As Ritz points out, the first two equations appear only to be particular cases of the form n I I N +1)2 in which s and r have the form given above. In the trunk series s has the particular value 1 5, and in the main branch series s  has the particular value 2, but we should expect a weaker set of lines to exist corresponding to the trunk series with r=2 5 or corresponding to the main branch series with s=3, and in fact a whole succession of such series. Taking the Trunk and Main Branch Series, we find they depend altogether on the four constants: al, b, a', b', while N is a universal constant identical with that deduced from the hydrogen series. As an example of the accuracy obtained we give in the following Table the figures for potassium. The lines of the trunk series are double but for the sake of shortness the least refrangible component is here omitted.

Trunk Series.

| 

Main Branch.

| 

Side Branch.  
  
---|---|---  
  
S

| 

n

| 

0

| 

r

| 

n

| 

0

| 

s

| 

n

| 

0  
  
2

| 

13036.8

| 

-0.24

| 

1'5

| 

12980.7

| 

000

| 

5

| 

17199.5

| 

ooo  
  
3

| 

24719'4

| 

+0.00

| 

2'5 

| | | 

6

| 

18709.5

| 

ooo  
  
4

| 

29006.7

| 

+0.12

| 

3.5

| 

14465.3

| 

000

| 

7

| 

19611.2

| 

+o16  
  
5

| 

31073.5

| 

-0.05

| 

4.5

| 

17288.3

| 

+0.20

| 

8

| 

20188.0

| 

+070  
  
6

| 

32226.5

| 

+0.40

| 

5.5

| 

18779.2

| 

+0.22

| | |   
  
7 

| 

32939'4

| 

-0.05

| 

6'5

| 

19662.3

| 

+0.22

| | |   
  
8 

| 

33408.7

| 

-o08

| 

7.5

| 

20224.7

| | | |   
  
9

| 

337362

| 

-0.07

| | | | | |   
  
10

| 

33971.4

| 

-0.23

| | | | | |   
  
I I n? -n ? =N -FM)

| 

2 ] =n1.  
  
---|---  
  
Spectrum of Potassium.  W. M. Hicks 1 has modified Rydberg's equation in a way similar to that of Ritz as shown by (5) above. This form has the advantage that the constants of the equation when applied to the spectra of the alkali metals show marked regularities. The most extensive series which has yet been observed is that of the trunk series of sodium when it is observed as an absorption spectrum; R. W. Wood has in that case measured as many as 50 lines belonging to this series.

The different series have certain characteristics which they seem to maintain wherever they have been obtained. Thus the trunk series consists of lines which are easily reversed while those of the side branch are nebulous. The lines of the trunk seem to appear at lower temperatures, which may account for the fact that it can be observed as absorption lines. If we compare together the spectra of the alkali metals, we find that the doublets of the branch series separate more and more as the wave-length increases. Roughly speaking the difference in frequency is proportional to the square of the atomic weight. Taking sodium and lithium we find in this way that the lithium lines ought to be double and separated by 7 A. They have not, however, so far as we know, been resolved. The roots of the three series have frequencies which diminish as the atomic weight increases, but not according to any simple law.

In the case of other metallic groups similar series have also been found, but while in the case of the alkali group nearly the whole spectrum is represented by the combined set of three series, such is not the case with other metals. The spectra of magnesium, calcium, zinc, cadmium and mercury, give the two branch series, and each series is repeated three times with constant difference of frequency. In these elements the doublets of the alkali series are therefore replaced by triplets. Strontium also gives triplets, but only the side branch series has been observed. In the spectrum of barium no series has yet been recognized. The spectrum of helium has been very carefully studied by Runge and Paschen. All its lines arrange themselves in two families of series, in other words, the spectrum looks like that of the superposition of two spectra similar to those presented by the alkali metals. Each family consists of the trunk, main branch and side branch. The conclusion which was originally drawn from this fact that helium is a mixture of two gases has not been confirmed, as one of the spectra of oxygen is similarly constituted.

We must refer to Kayser and Runge's Handbuch for further details, as well as for information on other spectra such as those of silver, thallium, indium and manganese, in which series lines have been found.

Before leaving the subject, we return for a moment to the spectrum of hydrogen. In 1896, Professor E. C. Pickering discovered in the structure of the star E Puppis a series of lines which showed a remarkable similarity to that of hydrogen having the same root. Kayser on examining the spectrum recognized the fact that the two series were related to each other like the two branch series, and this was subsequently confirmed. If we compare Balmer's formula with the general equation of Ritz, we find that the two can be made to agree if the ordinary hydrogen spectrum is that of the side branch series and the constants a', b, c and d are all put equal to zero.' In that case the main branch is found to represent the new series if a' and b 1 are also put equal to zero, so that n l r I I N = 4 - y2' where r takes successively the values 1.5, 2.5, 3.5A knowledge of the constants now determines the trunk series, which should be n I I N -  (I,5)2 The least refrangible of the lines of this series should have a wavelength 4687.88, and a strong line of this wave-length has indeed been found in the spectra of stars which are made up of bright lines, as also in the spectra of some nebulae. It seems remarkable, however, that we should not have succeeded yet in reproducing in the laboratory the trunk and main branch of the hydrogen spectrum, if the spectra in question really belong to hydrogen.

Considering the complexity of the subject it is not surprising that the efforts to connect theoretically the possible periods of the atom considered as a vibrating system have met with no considerable success. Two methods of investigation are available. The one endeavours to determine the conditions, which are consistent with our knowledge of atomic constitution derived from other sources, and lead to systems of vibration similar to those of the actual atom. We might then hope to particularize or modify these conditions so as to put them into more complete agreement. An attempt in that direction has been made with partial success by J. H. Jeans, 2 who showed that a shell-like constitution of the atom, the shells being electrically charged, 1 Proc. Roy. Soc. (1909), 83, p. 226 (abstract).

2 Phil. Mag. (1901), 2, p. 421.

would lead to systems of periods not unlike those of a series of lines such as is given by observation. The other method starts from the observed values of the periods, and establishes a differential equation from which these periods may be derived. This is done in the hope that some theoretical foundation may then be found for the equation. The pioneer in this direction is E. Riecke, 3 who deduced a differential equation of the 10th order. Ritz in the paper already mentioned follows in the footsteps of Riecke and elaborates the argument. On the whole it seems probable that the system of moving electrons, which according to a modern theory constitute the atom, is not directly concerned in thermal radiation which would rather be due to a few more loosely connected electrons hanging on to the atom. The difficulty that a number of spectroscopic lines seem to involve at least an equal number of electrons may be got over by imagining that the atom may present several positions of equilibrium to the electron, which it may occupy in turn. A collision may be able to throw the electrons from one of these positions to another. According to this view the different lines are given out by different molecules, and we should have to take averages over a number of molecules to obtain the complete spectrum just as we now take averages of energy to obtain the temperature. 4 If it should be confirmed that the period called N in the above investigation is the same for all elements, it must be intimately connected with the structure of the electron. At present the quantity of electricity it carries, and also its mass, may be determined, and we can therefore derive units of length and of mass from our electrical measurements. The quantity N may serve to fix the third fundamental unit. One further point deserves notice. Lord Rayleigh,' who has also investigated vibrating systems giving series of lines approaching a definite limit of " root," remarks that by dynamical reasoning we are always led to equations giving the square of the period and not the period, while in the equation representing spectral series the simplest results are obtained for the first power of the period. Now it follows from Rydberg's second law put on a more accurate basis by Ritz that in one case at any rate a negative period has reality and must be interpreted just as if it were positive. This looks indeed as if the square of the period were the determining quantity.

9\. Distribution of Frequencies in Band Spectra.  \- In many cases the spectra of molecules consist of lines so closely ruled together in groups as to give the appearance of continuous bands unless high resolving powers are employed. Such spectra seem to be characteristic of complex molecular structure, as they appear when compounds are raised to incandescence without decomposition, or when we examine the absorption spectra of vapours such as iodine and bromine and other cases where we know that the molecule consists of more than one atom. The bands often appear in groups, and such spectra containing groups of bands when viewed through small spectroscopes sometimes give the appearance of the flutings of columns. Hence the name " fluted spectra," which is sometimes applied. Each band, as has been stated, is made up of lines indicating highly homogeneous vibrations. A systematic study of the distribution of frequencies in these bands was first made by H. Deslandres,s who found that the successive differences in the frequencies formed an arithmetical progression.

If s represents the series of integer numbers the distribution of frequency may be represented by C+Bs2, where C and B are constants. The brightest line, for which s=o, is called the " head " of the band; and as s increases the lines diminish in intensity. The band fades towards the red or violet according as A is positive or negative, and the appearance is sometimes complicated by the fact that several sets of lines start from identical or closely adjoining heads. The equation which expressed " Deslandres' law " was only given by its author as an approximate one. The careful measurements of Kayser and Runge of the carbon bands show that the successive differences in the frequencies do (1900), I, p. 399.

4 Nature (1895), 51, p. 293.

Phil. Mag. (1897), 44, p. 356.

6 Comptes (1885), Ioo, p. 1256.

not quite keep up with the mathematical expression but tend to become more equal. The distances between the two first lines is A, and is small compared with the frequency itself, which is B.

If this is the case it is obvious that an equation of the form n=A - +a does, for small values of s, becomes identical with Deslandres' equation, a representing a constant which is large compared with unity. If we wish to be more general, while still adhering to Deslandres' law as a correct representation of the frequencies when s is small, we may write n - A (s+ 1 1) 2 - - a Po+Pi(s + c) -F +pr(s+ c)r' where s as before represents the integer numbers and the other quantities involved are constants. If r =1, we obtain Pickering's equation, which is the one advocated by Halm. Equations of this form have received a striking observational verification in so far as they predict a tail or root towards which the lines ultimately tend when s is increased indefinitely. This fact bridges over the distinction between the band and line spectra. The distance between the lines measured on the frequency scale does not, according to the equation, increase indefinitely from the head downwards, but has a maximum which, in Pickering's form as written above, is reached when (s + ,u) 2 = 3a. This gives a real value for s  only when a is positive. If a is negative the frequency passes through infinity and the maximum distance between the lines occurs there. If we only assign positive values to n and a, the band fades away from the head, the lines at first increasing in distance. It appears from the observations of A. S. King, that in the case of the so-called spectrum of cyanogen these tails can be observed. If a negative value of the frequency is admitted, more complicated effects may be predicted. A band might in that case fade away towards zero frequencies, and as s increases, return again from infinity with diminishing distances, the head and the tail pointing in the same direction; or with a different value of constants a band might fade away towards infinite frequencies, then return through the whole range of the spectrum to zero frequencies, and once more return with its tail near its head. The same band may therefore cross its own head on the return journey. If we adopt Thiele's view that each band is accompanied by a second branch for which s has negative values the complication is still further increased, but there does not seem to be sufficient reason to adopt this view.

ro. Effects of Varying Physical Conditions. - The same spectrum may show differences according to the physical conditions under which the body emitting the spectrum is placed. The main effects we have to discuss are (I) a symmetrical widening, (2) a shift of wave-length, which when it accompanies expansion in both directions may appear as an unsymmetrical widening, (3) a change in the relative intensities of the lines.

As typical examples illustrating the facts to be explained, the following may be mentioned. (a) When a sodium salt is placed in a Bunsen burner in sufficient quantity, the yellow lines are widened. When the amount of luminous matter is small the lines remain narrow. (b) If a spark be sent through a Plucker tube containing hydrogen the lines are widened when the pressure 1 Trans. Roy. Soc. Edin. (95), 41, 551.

2 Astrophys. Journ. (1897), 6, p. 65; (1898), 8, p.

Ibid. (1901), 14, p. 323.

is increased. (c) Under moderate pressures the lines of hydrogen may be widened by powerful sparks taken from a condenser. (d) If a spark be taken from an electric condenser through air, both the lines of oxygen and nitrogen are wide compared with what they would be at low pressures. But a mixture of nitrogen and oxygen containing only little nitrogen will show the nitrogen lines narrow and similarly narrow oxygen lines may be obtained if the quantity of oxygen is reduced. (e) If a spark be taken from a solution of a salt, e.g. lithium, the relative intensities of the lines are different according as the solution is concentrated or dilute. (f) The relative intensity of lines in the spark taken from metallic poles may be altered by the insertion of greater or smaller capacities, similarly the relative intensities are different in arc and spark spectra. (g)  Increased pressure nearly always diminishes the frequency of vibration, but this effect is generally of a smaller order of magnitude than the widening which takes place in the other cases. In investigating the effects of mixture on the widening of lines in absorption spectrum, R. W. Wood discovered some interesting effects. The cadmium line having a wave-length of 2288 A broadens by pressure equally in both directions, but if mercury be added the broadening is more marked on the less refrangible side.

The discussion as to the causes of this widening has turned a good deal on the question whether it is primarily due to changes of density, pressure or temperature, but some confusion has been caused by the want of proper definition of terms. For the cause of this the writer of the present article is jointly with others at any rate partly responsible, and clearness of ideas can only be re-established by investigating the mechanical causes of the effect rather than by applying terms which refer to a different order of physical conceptions.

The facts, as quoted, point to the closeness of the packing of molecules as the factor which always accompanies and perhaps causes the widening of lines. But is this alone sufficient to justify us in assigning the widening to increased density? Increased density at the same temperature means in the first place a reduction of the average distance between the molecules, but it means also a reduction in the mean free path and an increase in the number of impacts. The question is: which of these three factors is significant in the explanation of the widening? If it is the average distance irrespective of length of path and of number of impacts we should be justified in ascribing the effect to density, but if it is the number of impacts it would be more reasonable to ascribe it to pressure. The question could not be settled by experiments made at the same temperature, and if the temperature is altered the question is complicated by the distinction which would probably have to be drawn between the number of collisions and their intensity. Experimentally we should be confined to a strict investigation of absorption spectra, because in the electric discharge temperature has no definite meaning, and variations of pressure and density are not easily measured.

Assuming for a moment the change to be one of density and leaving out of account the pressure shift, the cases (e) and (f)  point to the fact that it is the closeness of packing of similar  molecules which is effective, e.g. the number of oxygen molecules per cubic centimetre determines the width of the oxygen lines, though nitrogen molecules may be mixed with them without materially affecting the appearance. Experiment (c) is, however, generally taken to mean that this closeness of packing cannot be the sole determining cause, for it is argued that if a closed vacuum tube can show both wide and narrow lines according to the mode of discharge, density alone cannot account for the change. But this argument is not conclusive, for though the total number of hydrogen molecules is fixed when the gas is enclosed, yet the number of luminous molecules may vary with the condition. Those that are not. luminous may, if they do not contain the same vibrating system, behave like inert molecules. When an electric current from a battery is sent through a tube containing hydrogen, increase of current simply means increase in the number of ions which take part where is an additional constant.

We have now reduced the law for the bands to a form which we have found applicable to a series of lines, but with this important difference that while a in the case of line spectra is a small corrective term, it now forms the constant on which an essential factor in the appearance of the band depends. Halm,' to whom we owe a careful comparison of the above equation with the observed frequencies in a great number of spectra, attached perhaps too much weight to the fact that it is capable of representing both line and band spectra. It is no doubt important to recognize that the two types of spectra seem to represent two extreme cases of one formula, the significant difference being that in the line spectrum the distance between lines diminishes as we recede from the head, while in the case of the band it increases, at any rate to begin with. But, on the other hand, no one pretends to have found the rigorous expression for the law, and the appropriate approximation may take quite different forms when constants which are large in one case are small in the other. It would not therefore be correct to push this agreement against Ritz's expression which is not applicable to bands.

A discussion of band spectra on a very broad basis was given by Thiele,' who recommends a formula - q +qi(s+c)+ +qr(s+c)r n in the discharge, except within the region of the kathode glow. Each molecule need not radiate with increased energy, but the more brilliant emission of light may be due to the greater number of particles forming similar vibrating systems.

When we compare together electric discharges the intensity of which is altered by varying, the capacity, we are unable to form an opinion as to whether the effects observed are due to changes in the density of the luminous material or changes of temperature, but the experiments of Sir William and Lady Huggins 1 with the spectrum of calcium are significant in suggesting that it is really the density which is also the determining factor in cases where different concentrations and different spark discharges produce a change in the relative intensities of different lines.

The widening of lines does not lend itself easily to accurate measurements; more precise numerical data are obtainable by the study of the displacements consequent on increased density which were discovered and studied by W. J. Humphreys and J. F. Mohler. In the original experiments 2 the pressures could only be increased to 15 atmospheres, but in a more recent work Humphreys,' and independently Duffield, were able to use pressures up to ioo atmospheres. The change of frequency (dn) for a series of lines which behave similarly is approximately proportional to the frequency (n) so that we can take the fraction do/n as a measure of the shift. It is found that the lines of the same element do not all show the same shift, thus the calcium line at 4223 is displaced by 0.4 A by ioo atmospheres pressure, while the H and K lines are only displaced through about half that amount. Duffield finds that the iron lines divide themselves into three groups with pressure shifts which are approximately in the ratio i: 2: 4. Curiously enough this is also approximately the ratio of the displacements found by Humphreys in the trunk series, the side branch and main branch in the order named, in cases where these displacements have been measured. It was believed that band spectra did not show any pressure shift, until A. Dufour' discovered that the lines into which the band spectra of the fluorides of the alkaline earths may be resolved widen towards the red under increased pressure.

Let us now consider the causes which may affect the homogeneity of radiation. We have first the Doppler effect, which, according to Michelson's experiment, is the chief cause of the limit at very low pressures, but it is too small to account for the widening which is now under discussion. We have further to consider the possibility of sudden changes of phrase during an encounter between two molecules, and we can easily form an estimate of the amount of apparent widening due to this cause. It is found to be appreciable but smaller than the observed effects.

Shortly after the discovery of pressure shifts A. Schuster suggested that the proximity of molecules vibrating in the same period might be the cause of the diminished frequency, and suggested that according to this view the shifts would be similar if the increase of density were produced by the presence of molecules of a different kind from those whose lines are being examined. Though there is no absolutely conclusive evidence, no experiments hitherto have given any indication that the nature of the gas producing the pressure has any effect on the amount of shift. G. F. Fitzgerald 6 suggested as an alternative explanation the change of inductive capacity of the medium due to increased density. J. Larmor 7 developed the same idea, and arrived by a very simple method at an approximation estimate of the shift to be expected.

If the medium which contains the vibration is divided into a sphere equal to k times the molecular vibration outside of which the effects of these molecules may be averaged up, so that its Roy. Soc. (1897), 61, p. 433.

Astrophys. Journ. (1876), 3, p. 114. Ibid. (2907), 26, p. 18.

Comptes rendus (1908), 146, pp. 118, 229\. Astrophys. Journ. (1896), 3, p. 292.

6 Ibid. (1897), 5, p. 210.

7 Ibid. (1907), 26, p. 120.

inductive capacity may be considered uniform and equal to K, the frequency of the vibration is increased in the ratio of the square root of 1 - le-"+3(1 -  K \- 1 ) to 2. Here n represents an integer which is 3 if the vibration is a simple doublet, but may have a higher integer value. If K has a value nearly equal to unity, the pressure shift is z k2 " +3 (K- 1 \- 1); and it is significant that for different values of n, the shifts should be in geometric ratio, because as stated above, the ratio occurring in the amounts observed with different lines of the same element are as 1: 2: 4. The question is complicated by the fact that in the cases which have been observed, the greater portion of the metallic vapour vibrates in an atmosphere of similar molecules, and the static energy of the field is determined by the value of K applicable to the particular frequency. It would therefore seem to be more appropriate to replace 1 - K- 1 by (2 - I)1112, where j s is the refractive index; but this expression involves the wave propagation for periods coinciding with free periods of the molecules. Close to and on either side of the absorptive band µ 2 has large positive and negative values, and if the above expression remains correct the change of frequency would, close to the centre of absorption, be 2 k-2"+3, which for n =3 and k= Io is 1/2000, or 500 times greater than the observed shifts, but this represents now the maximum displacement and not the displacement of the most intense portion of the radiation. There is a region within the band where µ = o, and this would give an infinite shift in the opposite direction. We therefore should expect a band in place of the line, which is the case, but our calculation is not able to give the displacement of the most intense portion, which is what we require for comparison with experiment.

The effects of resonance have been studied theoretically by Prince Galitzin s and later by V. W. Ekman. 9 The latter obtains results indicating no displacement but a widening. He concludes an interesting and important investigation by' giving reasons for believing that the centre of a widened line radiates with smaller energy than the adjacent parts. Hence the apparent reversals so frequently observed in the centre of a widened line may not be reversals at all but due to a reduction in luminosity. Ekman quotes in support an observation due to C. A. Young, according to which the dark line observed in the centre of each component of the sodium doublet in a Bunsen burner is transparent to a radiation placed behind. It should not be difficult to decide whether the reversals are real or fictitious.

Leaving the consideration of radical changes of a vibrating system out of account for the present, the minor differences which have been observed in the appearances of spectra under different sparking conditions are probably to a large extent due to differences in the quantities of material examined, though temperature must alter the violence of the impact and there is a possible effect due to a difference in the impact according as the vibrating system collides with an electron or with a body of atomic dimensions.

A. Schuster and G. A. Hemsalech have observed that the insertion of a self-induction in a condenser discharge almost entirely obliterates the air lines, and the same effect is produced by diminishing the spark gap sufficiently. The explanation of these facts presents no difficulty, inasmuch as during the sudden discharge which takes place in the absence of a self-induction, the metallic molecules have not sufficient time to diffuse through the spark gap; hence the discharge is carried by the gas in which it takes place. When, however, the time of discharge is lengthened, the conditions of the arc are more nearly approached. When the spark gap is small, the sudden evaporation of the metal has a better chance of filling the interval between the poles, even without the introduction of a self-induction.

Enhanced lines are lines which appear chiefly near the pole when strong spark discharges are used. Their presence indicates the characteristic difference between the spark and the arc. The name is due to Sir Norman Lockyer, who has studied these lines and drawn the attention of astronomers to their importance in interpreting stellar spectra. These lines in the case of the spark cannot be due entirely to the increased mass of vapour near the poles, but indicate a real change of spectrum probably connected with a higher temperature.

8 Wied. Ann. (1895), 56, p. 78.

9 Ann. d. Phys. (2907), 24, p. 580.

I 1. Molecular Velocities. - A. Schuster and G. A. Hemsalech 1 have measured the velocity with which the luminous molecules are projected from metallic poles when a strong spark is passed through the air interval which separates the poles. The method adopted consisted in photographing the spectrum on a film which was kept in rapid motion by being attached to the front of a rotating disk. The velocities ranged from about 400 to 1900 metres, the metals of small atomic weight giving as a rule the higher velocities. In the case of some metals, notably bismuth, the velocity measured was different for different lines, which seems intelligible only on the supposition that the metal vapour consists of different vibrating systems which can differ with different velocities. C. C. Schenck 2 subsequently conducted similar experiments, using a rotating mirror, and though he put a different interpretation on the effects, the main conclusions of Schuster and Hemsalech were not affected. These have further been confirmed and extended by the experiments of J. T. Royds made with the same rotating disk, but with improved optical appliances. The photographs taken by Royds show the separate oscillations of each spark discharge even when the circuit only contained the unavoidable capacity of the leads. It was found that during the successive electrical oscillations the metallic lines can be observed to stretch farther and farther away from the poles, thus giving a measure of the gradual diffusion of the metal. The subject wants further investigation, especially with a view to deciding the connexion between the molecular rush and the discharge. While some of the phenomena seem to indicate that the projection of metallic vapours into the centre of the spark is a process of molecular diffusion independent of the mechanism of the discharge, the different velocities obtained with bismuth, and the probability that the vibrating systems are not electrically neutral, seem to indicate that the projected metallic particles are electrified and play some part in the discharge.

## 12\. The Zeeman Ef f ect

The change of frequency of oscillation of radiating molecules placed in a magnetic field, which was discovered by P. Zeeman, and the observed polarization of the components, are all beautifully explained by the theory of H. A. Lorentz, and leave no manner of doubt that the radiating centres are negative electrons. The fact that in certain simple cases where a line when looked at equatorially splits into a triplet, the ratio of the charge to the mass is found by Lorentz's theory to be equal to that observed in the carrier of the kathode ray, shows that in these cases the electron moves as an independent body and is not linked in its motion to other electrons. On the other hand, most of the lines show a more complicated structure in the magnetic field, suggesting a system of electrons rather than a single free corpuscle. The question has been fully discussed by C. Runge in the second volume of Kayser's Handbuch (see also Magneto-Optics), and we may therefore content ourselves with the mention of the law discovered by Th. Preston that all the lines of the same series show identical effects when measured on the frequency scale, arfrl the fact recently announced by Runge 3 that even in the more complicated cases mentioned some simple relation between the distances of the components exists. If a is the distance shown by the normal triplets the type of separation observed in the line D2 shows distances from the central line equal to a /3, 3a/3, 5a/3, while the type of D 1 gives 2a/3, 4a/3. In all observed cases the distances are multiples of some number which itself is a sub-mutiple of a. The component lines of a band spectrum do not as a rule give the Zeeman effect, and this seems to be connected with their freedom from pressure shifts, for when Dufour had shown that the bands of the fluoride of calcium were sensitive to the magnetic field, R. Rossi 4 could show that they were also sensitive to pressure.

## 13\. Identification of Spectra

The interpretation of spectroscopic observation seemed very simple when Kirchhoff and 1 Phil. Trans. (1899), 190, p. 189.

2 Astrophys. Journ. (r90r), 14, p. 116. Phys. Zeitschrift, 8, p. 225.

Proc. Roy. Soc. (5909), 82, p. 518.

Bunsen first announced their discovery, for according to their view every combination of an element showed the characteristic spectrum of its constituent atoms; it did not matter according to this view whether a salt,' e.g. sodium chloride, introduced into a flame, was dissociated or not, as in either case the spectrum observed would be that of sodium. It was soon found, however, that compounds possess their own characteristic spectra, and that an element may give under special conditions of luminosity several different spectra. When we now speak of the identification of spectra we like to include, wherever possible, the identification of the particular compound which is luminous and even - though we have only begun to make any progress in that direction - the differentiation between the molecular or electronic states which yield the different spectra of the same element.

One preliminary question must first be disposed of. The fact that the gases with which we are most familiar are not rendered luminous by being heated in a tube to a temperature well above a white heat has often been a stumbling block and raised the not unreasonable doubt whether approximately homogeneous oscillations could ever be obtained by a mere thermal process. The experiment proves only the transparency of the gases experimented upon, and this is confirmed by the fact that bodies like bromine and iodine give on heating an emission spectrum corresponding to the absorption spectrum seen at ordinary temperatures. The subject, however, required further experimental investigation, which was supplied by Paschen. Paschen proved that the emission spectra of water vapour as observed in an oxyhydrogen flame ,and of carbon dioxide as observed in a hydrocarbon flame may be obtained by heating aqueous vapour and carbon dioxide respectively to a few hundred degrees above the freezing point. The same author proved that a sufficient thickness of layer raised the radiation to that of a black body in agreement with Kirchhoff's law. The spectra experimented on by Paschen were band spectra, but as these split up into fine lines the possibility of homogeneous radiation in pure thermal oscillation may be considered as established. Paschen's observations originated in the desire to decide the question raised by E. Pringsheim, who, by a series of experiments of undoubted merit, tried to establish that the emission of the line spectra of the alkali metals was invariably associated with a reduction of the metallic oxide. Pringsheim seems, however, to have modified his view in so far as he now seems to consider that the spectra in question might be obtained also in other ways, and to attach importance to the process of reduction only in so far as it forms an effective inciter of the particular spectra. In spite of the fact that C. Fredenhagen has recently attempted to revive Pringsheim's original views in a modified form - substituting oxidation for reduction - we may consider it as generally admitted that the origin of spectra lies with vibrating systems which are definite and not dependent on the method of incitement. These systems may only be semi-stable, but they must last a sufficient length of time to give a train of waves having a length corresponding to the observed homogeneity of the line.

In many cases there is a considerable difficulty in deciding whether a particular spectrum belongs to a compound body or to one of the elements composing the compound. Thus one of the most common spectra is that seen at the base of every candle and in every Bunsen burner. Everybody agrees that carbon is necessary for its appearance, but some believe it to be due to a hydrocarbon, others to carbon monoxide, and others to volatilized carbon. There is a vast amount of literature on the subject, but in spite of the difficulty of conceiving a luminous carbon vapour at the temperature of an ordinary carbon flame, the evidence seems to show that no other element is necessary for its production as it is found in the spectrum of pure carbon tetrachloride and certainly in cases where chlorine is excluded. Another much disputed spectrum is that giving the bands which appear in the electric arc; it is most frequently ascribed to cyanogen, but occasionally also to carbon vapour.

Compounds generally show spectra of resolvable bands, and if an elementary body shows a spectrum of the same type we are probably justified in assuming it to be due to a complex molecule. But that it may be given by the ordinary diatomic molecule is exemplified by oxygen, which gives in thick layers by absorption one of the typical sets of bands which were used by Deslandres and others to investigate the laws of distribution of frequencies. These bands appear in the solar spectrum as we observe it, but are due to absorption by the oxygen contained in the atmosphere.

If oxygen is rendered luminous by the electric discharge, a series of spectra may be made to appear. Under different conditions we obtain (a) a continuous spectrum most intense in the yellow and green, (b) the spectrum dividing itself into two families of series, (c) a spectrum of lines which appears when a strong spark passes through oxygen at atmospheric pressure, (d) a spectrum of bands seen in the kathode glow. We have therefore five distinct spectra of oxygen apart from the absorption spectra of ozone. To explain this great variability of spectroscopic effects we may either adopt the view that molecular aggregates of semi-stable nature may be found in vacuum tubes, or that a molecule may gain or lose one or more additional electrons and thus form new vibrating systems. It seemed that an important guide to clear our notions in this direction could be obtained through the discovery of J. Stark, who exa*r;ned the spectra of the so-called " canal-rays " (Canalestrahlen).  These rays are apparently the trajectories of positively charged particles having masses of the order of magnitude of the gaseous molecules. Stark discovered that in the case of the series spectrum of hydrogen and of other similar spectra the lines were displaced indicating high velocities; in other cases no displacements could be observed. The conclusion seemed natural that the spectra which showed the Doppler effect were due to vibratory systems which had an excess of positive charge. More detailed examinations of the " canal-rays " by J. J. Thompson and others have shown however that they contain both neutral and charged molecules in a relative proportion which adjusts itself continuously, so that even neutral molecules may partake of the translatory motion which they gained while carrying a charge. No conclusion can therefore be drawn, as Stark' has more recently pointed out, respecting the charge of the molecule which emits the observed spectrum. Nevertheless, the subject is well worth further investigation.

Previous to Stark's investigation P. Lenard 2 had concluded that the carriers of certain of the lines of the flame spectra of the alkali metals are positively charged. He draws a distinction between the lines of the trunk series to which he assigns neutral, and the lines of carriers the two branch series of which are electrically charged. The numerical relations existing between the trunk series and the branch series make it somewhat difficult to believe that they belong to different vibrating systems. But while we should undoubtedly hesitate on this ground to adopt Fredenhagen's 3 view that the two branch series belong to the element itself and the trunk series to a process of oxidation, we cannot press the argument against the view of Lenard, because the addition or subtraction of an electron introduces two vibrating systems which are still connected with each other and some numerical relationship is probable. Whatever ideas we may form on this point, the observations of Stark and Siegl 4 have shown that there is a Doppler effect, and therefore a positive charge, for one of the lines of the trunk series of potassium, and E. Dorn 5 has found the Doppler effect with a number of lines of helium, which contain representatives of the trunk series as well as of the two branch series. These facts do not countenance the view that there is an essential electric difference between the vibrating system of the three members of a family of series.

It is probable, however, that the above observations may 1 Phys. Zeitschrift (1910), IT, p. 171.

2 Ann. d. Phys. (1905), 1 7, p. 197.

3 Phys. Zeitschrift (1904), 8, p. 735.

4 Ann. d. Phys. (1906), 21, P. 457.

Phys. Zeitschrift (1907), 8, p. 589.

help to clear up some difficulties in the phenomena presented by flames. While we have seen that the radiation of sodium vapour has an intensity corresponding to that of the pure thermal radiation at the temperature of the flame, other flames not containing oxygen (e.g. the flames of chlorine in hydrogen) do not apparently emit the usual sodium radiation when a sodium salt is placed in them. In the light of our present knowledge we should look for the different behaviour in the peculiarity of the oxygen flame to ionize the metallic vapour.

14\. Fluorescence and Phosphorescence. - When a simple periodic force acts on a system capable of oscillatory motion the ultimate forced vibration has a period equal to that of the impressed force, but the ultimate state is only reached theoretically after an infinite time, and if meanwhile the vibrating system suffers any perturbations its free periods will at once assert themselves. Applying the reasoning to the case of a homogeneous radiation traversing an absorbing medium, we realize that the mutual disturbances of the molecules by collision or otherwise must bring in the free period of the molecule whatever the incident radiation may be. It is just in this degradation of the original period that (according to the present writer) the main phenomenon of absorption consists. 6 With most bodies the degradation goes on rapidly and the body mainly radiates according to its temperature, but there are cases in which these intermediate stages can be observed and the body seems then to be luminous under the influence of the incident radiation. Such bodies are said to be fluorescent, the degradation of motion towards that determined by its temperature gives rise to the law of Stokes, the fluorescent light being in nearly all cases of lower frequency than the incident light. With absorbing gases we should expect the degradation to proceed more slowly than with liquids, and hence the discovery of E. Wiedemann and Schmidt' that the vapours of sodium and potassium are fluorescent, important as it was from an experimental point of view, caused no surprise. It is not possible here to enter into a detailed description of the phenomena of fluorescence (q.v.), though their importance from a spectroscopic point of view has been materially increased through the recent researches of Wood s on the fluorescence of sodium vapour. After Wood and Moore had confirmed and extended the observations of Wiedemann and Schmidt and. showed that the vibrating system of the fluorescent light seems identical with that observed by absorption in the fluted band spectrum, Wood excited the fluorescence by homogeneous radiation and discovered some remarkable facts. The fluorescent bands in this case appear to shift rapidly when the period of the incident vibration is altered, though the change may be small. The author, no doubt correctly, remarks that the shift does net indicate a change of frequency but a change of relative intensity, consisting of a great number of fine lines; when the maximum intensity of the distribution of light is altered, the appearance is that of a shift. It would probably not be difficult to imagine a mechanical system having a number of free periods which when set into motion by a forced vibration shows a corresponding effect. If the forced vibration is suddenly stopped, the free periods will appear but not necessarily with the same intensity when the period of the original forced vibration is altered. There cannot, however, be a question that, as R. W. Wood remarks, the careful investigation of these phenomena is. likely to give us an insight into the mechanism of radiation.

Phosphorescence (q.v.) can only be here alluded to in order to draw attention to the phenomena studied by Sir William Crookes and others in vacuum tubes. When kathode rays strike certain substances, they emit a phosphorescent light, the spectroscopic investigation of which shows interesting effects which are important especially as indicating the influence of slight admixtures of impurities on the luminescence. It should be mentioned that the infra-red rays have a remarkable damping effect on the phenomena of phosphorescence, a fact which has.

s Schuster, Theory of Optics, p. 254' Wied. Ann. (2896), 57, P. 4473 R. W. Wood and Moore, Astrophys. Journ. (1903), 18, p. 95; R. W. Wood and Moore, Phil. Mag. (1905), 20, p. 513.

been made use of by Becquerel in his investigations of infra-red radiations.

15\. Relationship between the Spectrum of an Element and that of its Compounds. - In the present state of our knowledge we cannot trace any definite relationship between the spectrum of a compound body and that of its elements, and it does not even seem certain that such a relationship exists, but there is often a similarity between different compounds of the same element. The spectra, for instance, of the oxides and haloid salts of the alkaline earths show great resemblance to each other, the bands being similar and similarly placed. As the atomic weight of the haloid increases the spectrum is displaced towards the red.

It is in the case of the absorption spectra of liquids that we can most often discover some connexion between vibrations of a complex system and that of the simpler systems which form the complex. The most typical case in this respect is the effect of a solvent on the absorption spectrum of a solution. A. Kundt,' who initiated this line of investigation, came to the conclusion that the absorption spectra of certain organic substances like cyanin and fuchsin were displaced towards the red by the solvent, and that the displacement was the greater the greater the dispersive power of the solvent. This law cannot be maintained in its generality, but nevertheless highly dispersive substances like carbon bisulphide are always found to produce a greater shift than liquids of smaller dispersion like water and alcohol. In these cases the solvent seems to act like an addition to the mass of the vibrating system, the quasi-elastic forces remaining the same.

Dr J. H. Gladstone, 2 at an early period of spectroscopy, examined the absorption spectra of the solution of salts, each constituent of which was coloured. He concluded that generally but not invariably the following law held good: " When an acid and a base combine, each of which has a different influence on the rays of light, a solution of the resulting salt will transmit only those rays which are not absorbed by either, or, in other words, which are transmitted by both." He mentioned as an important exception the case of ferric ferrocyanide, which, when dissolved in oxalic acid, transmits the rays in great abundance, though the same rays be absorbed both by ferrocyanides and by ferric salts. Soret has confirmed, for the ultra-violet rays, Dr Gladstone's conclusions with regard to the identity of the absorption spectra of different chromates. The chromates of sodium, potassium and ammonium, as well as the bichromates of potassium and ammonium, were found to give the same absorption spectrum. Nor is the effect of these chromates confined to the blocking out simply of one end of the spectrum, as in the visible part, but two distinct absorption bands are seen, which seem unchanged in position if one of the above-mentioned chromates is replaced by another. Chromic acid itself showed the bands, but less distinctly, and Soret does not consider the purity of the acid sufficiently proved to allow him to draw any certain conclusions from this observation.

In many of these cases the observed facts might perhaps be explained by dissociation, the undissociated compound producing no marked effect on the spectra. In 1872 W. N. Hartley and A. K. Huntingdon examined by photographic methods the absorption spectra of a great number of organic compounds. The normal alcohols were found to be transparent to the ultraviolet rays, the normal fatty acids less so. In both cases an increased number of carbon atoms increases the absorption at the most refrangible end. The fact that benzene and its derivatives are remarkable for their powerful absorption of the most refrangible rays, and for some characteristic absorption bands appearing on dilution, led Hartley to a more extended examination of some of the more complicated organic substances. He determined that definite absorption bands are only produced by substances in which three pairs of carbon atoms are doubly linked together, as in the benzene ring. Subsequently 3 he subjected the ultra-violet absorption of the alkaloids to a careful 1 Wied. Ann. (1878), 4, p. 34. Phil. Mag. (1857), 1 4, p. 418.

Phil. Trans. (1885), pt. ii.

investigation, and arrived at the conclusion that the spectra are sufficiently characteristic to " offer a ready and valuable means of ascertaining the purity of the alkaloids and particularly of establishing their identity." We can only briefly refer to an important investigation of Sir William Abney and Colonel E. R. Festing, who examined the infra-red absorption of a number of substances. We may quote one of the principal conclusions at which they arrived: " An inspection of our maps will show that the radical of a body is represented by certain well-marked bands, some differing in position according as it is bonded with hydrogen, or a halogen, or with carbon, oxygen or nitrogen. There seem to be characteristic bands, however, of any one series of radicals between woo and about i roo, which would indicate what may be called the central hydrocarbon group, to which other radicals may be bonded. The clue to the composition of a body, however, would seem to lie between 700 and woo. Certain radicals have a distinctive absorption about 700 together with others about 900, and if the first be visible it almost follows that the distinctive mark of the radical with which it is connected will be found. Thus in the ethyl series we find an absorption at 740, and a characteristic band, one edge of which is at 892 and the other at 920. If we find a body containing the 740 absorption and a band with the most refrangible edge commencing at 892, or with the least refrangible edge terminating at 920, we may be pretty sure that we have an ethyl radical present. So with any of the aromatic group; the crucial line is at 867. If that line be connected with a band we may feel certain that some derivative of benzene is present. The benzyl group shows this remarkably well, since we see that phenyl is present, as is also methyl. It will be advantageous if the spectra of ammonia, benzene, aniline and dimethyl aniline be compared, when the re-' markable coincidences will at once become apparent, as also the different weighting of the molecule. The spectrum of nitrobenzene is also worth comparing with benzene and nitric acid. In our own minds there lingers no doubt as to the easy detection of any radical which we have examined,. and it seems highly probable by this delicate mode of analysis that the hypothetical position of any hydrogen which is replaced may be identified, a point which is of prime importance in organic chemistry. The detection of the presence of chlorine or bromine or iodine in a compound is at present undecided, and it may be well that we may have to look for its effects in a different part of the spectrum. The only trace we can find at present is in ethyl bromide, in which the radical band about 90o is curtailed in one wing. The difference between amyl iodide and amyl bromide is not sufficiently marked to be of any value." The absorption spectra of cobalt and didymium salts also offer many. striking examples of minor changes produced in spectra by combination and solution. (A. S.*) Apparatus. - Spectroscopes may be divided into two classes: prism spectroscopes, with angular or direct vision, and grating spectroscopes; the former acting by refraction (q.v.), the latter by diffraction or interference. Angular prism spectroscopes are the commonest. Such an instrument consists of a triangular prism set with its refracting edge vertical on a rigid platform attached to a massive stand. The prism may be made of a dense flint glass or of quartz if the ultra-violet is to be explored, or it may be hollow and filled with carbon bisulphide, a-bromnaphthalene or other suitable liquid. Liquid prisms, however, suffer from the fact that any change of temperature involves a change in the refractive index of the prism. The stand carries three tubes: the collimator, observing telescope and scale telescope. The collimator has a vertical slit at its outer end, the width of which may be regulated by a micrometer screw; in some instruments one half of the slit is covered by a small total reflection prism which permits the examination of two spectra simultaneously. At the other end of the collimator there is a condensing lens for bringing the rays into parallelism. The observing telescope is of the ordinary terrestrial form. The scale telescope contains a graduated scale which is illuminated by a small burner; the scale is viewed by reflection from the prism face opposite the first refracting face. The power may be increased, but with a diminution of intensity, by using a train of prisms. Steinheil made an instrument of four prisms, each of which had, however, to be set in the position of minimum deviation by trial. In Browning's form the setting is automatic. The dispersion may be further increased by causing the rays to pass more than once through the prism or prisms. Thus, by means of a system of reflecting prisms, Hilger passed the dispersed rays six times through one prism, and, by similar means, Browning passed the rays first through the upper part of a train and then back through the lower part. Compound prisms are also employed. Rutherfurd devised one made of flint glass with two crown glass compensating prisms; whilst Thallon employed a hollow prism containing carbon bisulphide also compensated by flint glass prisms. In direct vision spectroscopes the refracting prisms and slit are in the observing telescope. The prisms are necessarily compound, and usually consist of flint glass with compensating prisms of crown. In all cases where compound prisms are used, the angles must be accurately calculated. Amici in 1860 devised such an instrument; an improved form by Jannsen was made up of two flint and three crown prisms, and in Browning's form there are three flint and four crown. Sorby and, later, Abbe, designed instruments on the same principle to be used in connexion with the microscope. By suitably replacing the ocular of the observing telescope in an angular vision spectroscope by a photographic camera, it is possible to photograph spectra; such instruments are termed spectrographs. In grating spectroscopes both plane and concave gratings are employed in connexion with a collimator and observing telescope.

## AuTxoRITIEs

The standard work is H. Kayser, Handbuch der Spectroscopie (1900-1910, vol. v.). See also J. Landauer, Spectrum Analysis (Eng. trans. by J. B. Tingle, 1898); E. C. C. Baly, Spectroscopy (1905). For spectra see A. Hagerbach and H. Konin, Atlas of Emission Spectra (Eng. trans. by A. S. King, 1905); F. Exner and E. Haschek, Wellenlcingen-Tabellen (1902-1904); W. M. Watts, Index of Spectra; also reports of B.A. Special Committee.